Solve for $x$ and $y$ using elimination. $\begin{align*}-7x+9y &= 9 \\ 8x+6y &= 6\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $3$ $\begin{align*}14x-18y &= -18\\ 24x+18y &= 18\end{align*}$ Add the top and bottom equations. $38x = 0$ Divide both sides by $38$ and reduce as necessary. $x = 0$ Substitute $0$ for $x$ in the top equation. $-7( 0)+9y = 9$ $9y = 9$ $9y = 9$ $y = 1$ The solution is $\enspace x = 0, \enspace y = 1$.